This invention relates generally to non-destructive or non-invasive evaluation of a multi-material object and, more specifically, to methods for generating data for performing Electrical Impedance Tomography of an object comprising different materials within a closed boundary, referred to as a multi-material object.
The principles of Electrical Impedance Tomography (EIT) are based on knowledge that objects under examination have variations in electrical properties, e.g., conductivities and permittivities, which are highly correlated with material characteristics such as density or chemical composition. For example, in the human body there are significant variations in electrical conductivity among body tissues.
In industrial activities and other non-clinical applications, it is desirable to perform non-invasive monitoring or imaging to determine the composition of a body volume, or to characterize the size and shape of a feature, or other condition within an object of interest. Generally, EIT is useful for imaging features within a volume that are characterized by distinguishable electrical properties. However, EIT can also be used in a manner where, instead of generating an image, the end-result may be a mathematical value or a set of mathematical values indicative of the location, proportions or other properties of the different materials within the volume. For example, features within volumes having different densities can be resolved on this basis. For example, in multiphase fluid mixtures it is known that conductivities will vary based on phase (e.g., liquid or gas) or chemical composition. In principle, electrical measurements performed with relatively simple instrumentation can provide data indicative of (i) where in the volume a particular material is located, (ii) the relative proportions of different constituents and (iii) the shape of the boundary between different materials within the volume. Examples of mixtures for which phase concentrations can be determined are solid-liquid compositions such as slurries, gas-liquid compositions such as present in oil pipelines, and, generally, liquid-liquid and solid-gas-liquid mixtures. The mixtures may be stationary or flowing. In the case of fluids flowing through a pipe, conductivity determinations among materials of different phases, or between materials having different chemical properties (e.g., water and oil), can lead to determinations of relative volumes present.
Generally, there is a need to determine internal flow characteristics in these types of multiphase flow processes as this information enables improved design and control of industrial processes and increased operational efficiency of existing and new processing equipment. Flow characteristics used to predict performance of multiphase processes may include, for example, spatial distributions of the phases (spatial volumetric phase fractions), flow regimes, definition of interfacial areas, and determination of absolute and relative velocities between the phases or materials. Knowing the spatial distribution of the materials is particularly useful since non-uniform distributions of the materials tend to reduce the interfacial area between materials available for chemical reaction or conversion and may result in recirculating flows creating spatially non-uniform reaction zones or concentrations. Further, the volumetric phase fraction and velocity are important parameters that enable proper and timely control of multiphase flows.
With respect to determining volume fractions of liquid and gas phases in a pipe using EIT, it is conventional to acquire data by placing a series of electrodes along the periphery of a body under study, e.g., in a circle along an interior surface of a pipe. See U.S. Pat. Nos. 4,486,835; 4,539,640; 4,920,490; and 5,381,333, all of which are incorporated herein by reference. In the systems described by the foregoing literature, a set of electrical signals (voltage or current) are applied to the volume via electrodes. The measured electrical signals (voltage or current) are used to reconstruct spatial features within the volume under study so that an image representative of the features can be generated. In this regard, there is what is often referred to as an inverse problem wherein there may not be a unique solution, i.e., image, corresponding to the acquired data. The set of applied electrical signals is typically a series of excitation patterns. It is necessary to sequentially drive the set of electrodes with a relatively large series of such excitation patterns. As an example, in one of the excitation patterns in the series all the electrodes may be applied with sinusoidal voltage signals that are phase shifted with respect to one another. Corresponding current signals are measured in response to each set of excitation patterns. Using data acquired from application of the series of excitation patterns, algorithms are applied to find a distribution of electrical properties within the volume and hence the distribution of various materials.
When the electrodes are positioned along a selected plane cutting through the body under study, the algorithms are intended to provide a distribution of the electrical properties along the same plane. Generally, a wide variety of mathematical methods and numerical techniques have been applied to determine the distribution of electrical properties representative of the multi-material object along the selected plane. Noting that currents spread into the third dimension (out of the plane along which the electrodes are placed) as they travel through a structure under examination, details of fine structures may not be easily resolved.